1998 - Draper Laboratory

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% Coverage908580757065Two-way Coverage-Ellipso 8:1600 100 200 300 400 500 600 700 800Days Since Epoch (Epoch:1 Jan 97)Figure 7. Ellipso TM two-way coverage (uncontrolled Borealis TM 8:1node at noon/midnight and Concordia).Case 1: Node at Noon/Node at MidnightNorthern Hemisphere 0-90N degSouthern Hemisphere 0-55S degThe baseline Ellipso TM constellation places the Borealis TM planes inthe Node at Noon/Node at Midnight configuration. Our analysisof this configuration will use the orbit maintenance requirementsidentified in Table 4. We will attempt to meet these requirementsby using the specialized targeting methods for the 8:1 EllipsoBorealis TM configuration identified earlier. (It should be noted that“shooting” methods meet these and stricter bounds, but withsignificantly greater fuel use.) The station-keeping strategy willattempt to stay within the required limit of the nominal referencetrajectory. These are the refined orbits defined by Sabol, withepoch mean element sets in Table 2. These epochs arepropagated by the DSST orbit generator in the presence of zonalharmonic and third-body perturbations to create the nominalreference trajectory. The actual trajectories will start with thesame initial elements, but will be propagated with zonalharmonics, tesseral resonance harmonics, third-body point mass,solar radiation pressure, and atmospheric drag. The DSST willuse Schatten’s “hot” predictions to calculate atmospheric densityfor the drag perturbation.The station-keeping algorithms were applied for the 5-yr EllipsoBorealis TM mission lifetime. The station-keeping budgets thatwere generated by ASKS for this case are shown in Tables 5 and6. Note that we control mean anomaly to ensure proper phasingbetween satellites by adjusting the semimajor axis. At eachmaneuver, the eccentricity is also controlled. When theatmosphere is hottest, the numerous drag make-ups have theeffect of tightly controlling the mean anomaly. The inclinationcorrections and resulting action on the node for the Node atMidnight plane are shown in Figures 8 and 9. Note that one ofthe satellites (Sat. 3) does not need a second inclination burn tocontrol the node. This is related to placement in the plane, andto tesseral resonance. Also notice that the inclination burns causethe node, Ω, to both overshoot and undershoot the limit (0.2 deg)by a small amount. This is due to the explicit analytical estimateof ∆I at each node violation. Since large (~10.0 m/s) burns arerequired for inclination burns, it will be desirable to refine thisrequired ∆I more precisely if this approach is used operationally.In Figures 10 and 11, one-way and two-way coverage plots for thecontrolled Node at Noon/Node at Midnight 8:1 EllipsoBorealis TM /Concordia constellation is shown for the first two yearsof the mission. It can be seen that 100-percent one-way coverageTable 5. 8:1 Borealis TM node at noon 5-yr Delta-V budget.Table 6. 8:1 Borealis TM node at midnight 5-yr Delta-V budget.Table 4. Borealis TM maximum orbital element limits.Automated Station-Keeping for Satellite Constellations9
is maintained in the Northern Hemisphere and nearly 98 percentin the Southern Hemisphere (north of 5ºS), while two-waycoverage is maintained at 85.5 percent in the North and 81.5percent in the South. This indicates that one of the goals ofsatellite station-keeping is met, i.e., continuous coverage ismaintained consistently.Case 2: 81:10 Node at Noon/Node at MidnightThe 81:10 repeat ground track mode is significantly different fromthe 8:1, with deep resonance perturbations removed so that allsatellites within a plane experience essentially the same averagedynamical environment. Consider, for example, the difference insemimajor axis between the nominal 81:10 trajectory and thefully perturbed trajectory over the 5-yr Ellipso Borealis TM missionlifetime shown in Figure 12. This is the Node at Midnight plane.Note that the divergence from nominal of the semimajor axis isindistinguishable between members of the same plane. (TheNode at Noon orientation has similar behavior.) This suggeststhat the mean anomaly separation between satellites within theplane will remain relatively stable. This is a case in which“formation flying” control algorithms may prove beneficial.The control strategy used for the 8:1 repeat ground track nolonger applies readily to the 81:10 case. In particular, the 8:1strategy takes advantage of the constant inclination rate due totesseral resonance to control nodal drift. This natural motiondoes not occur in the 81:10, where the inclination is stable overthe constellation lifetime. This is a positive byproduct of the81:10 design. The question arises: how well does this0.06Inclination Diff from Ref100.5One-Way Coverage-Ellipso 8:10.041000.0299.5INC Diff (deg)0-0.02% Coverage9998.5-0.04-0.060 2000 4000 6000 8000 10000 12000 14000 160009897.50Northern Hemisphere 0-90N degSouthern Hemisphere 0-55S deg20 40 60 80 100 120 140 160 180 200Time (97/01 to 99/01)Figure 8. Inclination error: 1 Jan. 1997 to 1 Jan. 2002(Borealis TM 8:1 node at midnight).Figure 10. One-way coverage: 1 Jan. 1997 to 1 Jan. 1999(8:1 Ellipso Borealis TM node at noon/midnight and Concordia).Acending Node Diff from RefTwo-Way Coverage-Ellipso 8:10.2585.50.2850.1584.50.184LAN Diff (deg)0.050-0.05% Coverage83.583-0.182.5-0.1582-0.2-0.250 2000 4000 6000 8000 10000 12000 14000 1600081.5810Northern Hemisphere 0-90N degSouthern Hemisphere 0-55S deg20 40 60 80 100 120 140 160 180 200Time (97/01 to 99/01)Figure 9. Ascending node error: 1 Jan. 1997 to 1 Jan. 2002(Borealis TM 8:1 node at midnight).Figure 11. Two-way coverage: 1 Jan. 1997 to 1 Jan. 1999(8:1 Ellipso Borealis TM node at noon/midnight and Concordia).Automated Station-Keeping for Satellite Constellations10
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Letter from thePresident and CEO,Vi
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Information TechnologyMilton AdamsE
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BiographyMilton Adams has been at D
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Figure 1 represents a functional de
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Programs. In effect, these controll
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Although the terminal area traffic
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Table 2. ATFM performance evaluatio
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In the experiments, a nominal capac
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[3] Wambsganss, Michael C. “Colla
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Guidance, Navigation, and Control A
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A Control Lyapunov FunctionApproach
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x( 0) ∈ X and w(t) ∈Wfor all t
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(b) Select a quadratic RCLF V i (x)
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at each grid point. In the case w 1
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References[1] Ball, J.A. and A.J. v
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Relative and Differential GPSData T
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Page 39 and 40: H R# δρ R,GPS -H A# δρ A,GPSThi
Page 41 and 42: selection; and (3) shown that the a
Page 43 and 44: Guidance, Navigation, and Control A
Page 45 and 46: Segmentation of MR ImagesUsing Curv
Page 47 and 48: (3)where ν now represents a contin
Page 49 and 50: Experimental ResultsThe results of
Page 51 and 52: Table 1. A summary of segmentation
Page 53 and 54: Guidance, Navigation,and ControlJim
Page 55 and 56: BiographyGeorge SchmidtGeorge Schmi
Page 57 and 58: clock and ephemeris errors, as well
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Page 61 and 62: Table 5. “Typical” absolute GPS
Page 63 and 64: performed, then the target location
Page 65 and 66: tightly-coupled system, however, ca
Page 67 and 68: Concluding RemarksRecent progress i
Page 69 and 70: As real-time systems evolve into th
Page 71 and 72: Advanced Fault-TolerantComputing fo
Page 73 and 74: The Viking and Voyager were both in
Page 75 and 76: Containment Regions (FCRs). There a
Page 77 and 78: well as reversing the whole process
Page 79 and 80: As real-time systems evolve into th
Page 81 and 82: Automated Station-Keepingfor Satell
Page 83 and 84: Figure 2. Minimum elevation angles
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Page 91 and 92: autonomy. It must have the ability
Page 93 and 94: [31] Neelon, Joseph G., Jr., Paul J
Page 95 and 96: Draper’s primary goal is to Drape
Page 97 and 98: )Rotordynamic Modelingof an Activel
Page 99 and 100: Eq. (9) becomes:λ[ R ] { Φ } = [
Page 101 and 102: chosen to be 24, for a total of 48
Page 103 and 104: InertialInstruments/MechanicalDesig
Page 105 and 106: BiographyJeffrey Borenstein is curr
Page 107 and 108: process step. Process information i
Page 109 and 110: Figure 4. Control chart for boron d
Page 111 and 112: References[1] Barbour, N., J. Conne
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Page 117 and 118: calculates miscellaneous terms, suc
Page 119 and 120: Table 1. Suggested specification sh
Page 121 and 122: User Accuracy as aFunction of Simul
Page 123 and 124: 20-min averaging, this clock lockin
Page 125 and 126: Table 2. Sample high-level summary
Page 127 and 128: AcknowledgmentR.L. Greenspan, J.A.
Page 129 and 130: Systems IntegrationRich MartoranaPe
Page 131 and 132: BiographyAnthony Kourepenis is an A
Page 133 and 134: control is employed to maintain the
Page 135 and 136: Table 1. Summary of automotive yaw
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References[1] Greiff, P., B. Boxenh
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An Integrated Safety AnalysisMethod
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Infrastructure ModelsSystemRequirem
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Figures 6 and 7 illustrate the bloc
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Notice that each flight track descr
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Table 7. Safety statistics at 1700-
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An Optimal Guidance Law forPlanetar
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Note that the states in the three d
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Crossrange (Kft)10090807060504030Cl
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The 1997 Charles StarkDraper PrizeT
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The 1997 Charles StarkDraper Prize1
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“Draper encourages its personnel
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Gimballed Vibrating GyroscopeHaving
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Optical Source Isolator withPolariz
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Hunting Suppressor forPolyphase Ele
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Sensor Having an Off-Frequency Driv
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proof mass from transients and enha
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1997 Published PapersThe following
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monitoring of space structures and
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measured by kinematic degrees of fr
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i.e., what percent of the earth’s
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McConley, M. W.; Dahleh, M. A.; Fer
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unaffordable, or even misguided. Bu
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The Draper DistinguishedPerformance
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Educational Activitiesat Draper Lab
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1998 - Draper Laboratory

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